The sum of two numbers is $98$, and their difference is $30$. What are the two numbers?
Answer: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 98}$ ${x-y = 30}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 128 $ $ x = \dfrac{128}{2} $ ${x = 64}$ Now that you know ${x = 64}$ , plug it back into $ {x+y = 98}$ to find $y$ ${(64)}{ + y = 98}$ ${y = 34}$ You can also plug ${x = 64}$ into $ {x-y = 30}$ and get the same answer for $y$ ${(64)}{ - y = 30}$ ${y = 34}$ Therefore, the larger number is $64$, and the smaller number is $34$.